A few additions to zippy13's excellent post:
* G Bignotti is probably the firm that made the barrels, apparently EIG does not make their own barrels.
* PSF is the smokeless proof mark from test firing, FINITO (means "finished") is applied when the proofing is done to the complete gun, meaning the barrels are not proofed prior to assembly.
* The name EIG has been used by several firearms manufacturers in different countries, generally adding to the confusion about these firearms.
* Further confusion comes from the fact that many firearms companies in Italy, including the Val Gardone and Brescia areas, assemble firearms from parts provided by specialty shops (barrelmakers, stock makers, lock makers, etc), or have the firearms assembled by such shops and just package them and ship them under their own name. This does not detract from the quality of those firearms, but it does make people a little leary of them due to the prospect of trying to find parts in case they are needed.